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Modified Model of RLS Adaptive Filter for Noise Cancellation

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Abstract

Recursive Least Square (RLS) is a popular algorithm for noise cancellation in non-stationary signals; however, it demands more computational resources and more difficult mathematical operations. Also, RLS has less performance stability. The present research explores a novel idea of an RLS adaptive noise cancellation through a modified method that uses an RLS adaptive filter by introducing an additional constant multiplier, along with their in-depth analysis. The proposed algorithm is analyzed using three primary performance metrics: mean square error (MSE), signal-to-noise ratio (SNR), and convergence rate. The obtained results demonstrate that the proposed algorithm has reduced the MSE by 79.65%, which leads to an improvement in SNR by 86.16% compared to the traditional RLS algorithm. The additional constant multiplier is optimized for SNR, and the optimized value is found to be equal to 0.65, which gives the best possible SNR value of 19.38 dB. Also, the proposed algorithm has been successfully applied to a real-world scenario in acoustic echo cancellation (AEC). The experimental setup for the echo canceller is simulated on MATLAB to measure the echo canceller efficiency in terms of MSE and echo return loss enhancement. Based on performance evaluation, the proposed algorithm has been found to better echo cancellation in AEC as compared to traditional RLS.

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Data Availability

The datasets generated during and/or analyzed during the current study are available on reasonable request.

References

  1. F. Akingbade, I. Alimi, Acoustic echo cancellation using modified normalized least mean square adaptive filters. Int. J. Sci. Eng. Res. 5(5), 1175–1179 (2014)

    Google Scholar 

  2. Albu, F., Improved variable forgetting factor recursive least square algorithm, in 12th International Conference on Control Automation Robotics & Vision (ICARCV). IEEE, (2012). https://doi.org/10.1109/ICARCV.2012.6485421

  3. F. Albu, C. Palelologu, A recursive least square algorithm for active noise control based on the Gauss-Seidel method, in 15th IEEE International Conference on Electronics, Circuits and Systems. IEEE, (2008). https://doi.org/10.1109/ICECS.2008.4674982

  4. V. R.Balaji, P.S. Surabhi, An Investigation on Under water images of hydroacoustic environment using RLS algorithm, in 4th International Conference on Inventive Research in Computing Applications (ICIRCA) IEEE, (2022) p. 1307–1311. https://doi.org/10.1109/ICIRCA54612.2022.9985704

  5. K.R. Borisagar, G.R. Kulkarni, Simulation and comparative analysis of LMS and RLS algorithms using real time speech input signal. Glob. J. Res. Eng. 10(5), 44–47 (2010)

    Google Scholar 

  6. Y. Chen, G. Yuantao, O.H. Alfred, Sparse LMS for system identification, in IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, (2009), p. 3125–3128. https://doi.org/10.1109/ICASSP.2009.4960286

  7. J. Chhikara, J. Singh, Noise cancellation using adaptive algorithms. Int. J. Mod. Eng. Res. (IJMER) 2(3), 792–795 (2020)

    Google Scholar 

  8. C. Dai, J. Wang, J. Xie, W. Li, Y. Gong, Y. Li, Removal of ECG artifacts from EEG using an effective recursive least square notch filter. IEEE Access. 7, 158872–158880 (2019). https://doi.org/10.1109/ACCESS.2019.2949842

    Article  Google Scholar 

  9. R. Dallinger, R. Markus, On robustness of coupled adaptive filters. in IEEE International Conference on Acoustics, Speech and Signal Processing IEEE, (2009) p. 3085–3088. https://doi.org/10.1109/ICASSP.2009.4960276

  10. H. Deng, M. Doroslovacki, Proportionate adaptive algorithms for network echo cancellation. IEEE Trans. Signal Process. 54(5), 1794–1803 (2006). https://doi.org/10.1109/TSP.2006.872533

    Article  Google Scholar 

  11. P.S.R. Diniz, Adaptive filtering (Germany, Springer, Berlin, 1997)

    Book  Google Scholar 

  12. S. Dixit, N. Deepak, Hardware reduction in cascaded LMS adaptive filter for noise cancellation using feedback. Circuits Syst., and Signal Process. 38, 930–945 (2019). https://doi.org/10.1007/s00034-018-0896-3

    Article  Google Scholar 

  13. S. Dixit, N. Deepak, LMS adaptive filters for noise cancellation: a review. Int. J. Electr. Comput. Eng. (IJECE) 7(5), 2520–2529 (2017). https://doi.org/10.11591/ijece.v7i5.pp2520-2529

    Article  Google Scholar 

  14. D.L. Duttweiler, Proportionate normalized least-mean-squares adaptation in echo cancelers. IEEE Trans. Speech Audio Process. 8(5), 508–518 (2000). https://doi.org/10.1109/89.861368

    Article  Google Scholar 

  15. E. Eleftheriou, D. Falconer, Tracking properties and steady-state performance of RLS adaptive filter algorithms. IEEE Trans. Acoust. Speech Signal Process. 34(5), 1097–1110 (1986). https://doi.org/10.1109/TASSP.1986.1164950

    Article  Google Scholar 

  16. C. Elisei-Iliescu, C. Paleologu, J. Benesty, C. Stanciu, C. Anghel, S. Ciochina, Recursive least-squares algorithms for the identification of low-rank systems. IEEE/ACM Trans. Audio, Speech, Lang Process. 27(5), 903–918 (2019). https://doi.org/10.1109/TASLP.2019.2903276

    Article  Google Scholar 

  17. D.A. Florêncio, S.M. Henrique, Multichannel filtering for optimum noise reduction in microphone arrays. in IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings, (2001), 197–200.https://doi.org/10.1109/ICASSP.2001.940801

  18. J. Fraden, Noise in sensors and circuits, in Handbook of Modern Sensors. (Springer, New York, 2015), pp.204–212. https://doi.org/10.1007/978-1-4419-6466-3

    Chapter  Google Scholar 

  19. J.G. Harris, J. Jui-Kuo, C.P. Jose, Analog hardware implementation of continuous-time adaptive filter structures. Analog Integr. Circ. Sig. Process 18, 209–227 (1999). https://doi.org/10.1023/A:1008363406175

    Article  Google Scholar 

  20. S. Haykin, B. Widrow, Least-Mean-Square Adaptive Filters (John Wiley & Sons. Inc, New Jersey, 2003). https://doi.org/10.1002/0471461288

    Book  Google Scholar 

  21. S.S. Haykin, Adaptive systems for the signal process, in Advanced Signal Processing Theory and Implementation for Sonar Radar and Non-Invasive Medical Diagnostic Systems, 2nd edn., ed. by S. Stergiopoulos (CRC Press, Boca Raton, 2017). https://doi.org/10.4324/9781315219042

    Chapter  Google Scholar 

  22. S.S. Haykin, Adaptive Filter Theory (Pearson Education India, Bangalore, 2008)

    Google Scholar 

  23. R.A. Horn, C.R. Johnson, Matrix analysis (Cambridge University Express, Cambridge, 1985), p.561. https://doi.org/10.5555/5509

    Book  Google Scholar 

  24. M. Kalamani, S. Valarmathy, M. Krishnamoorthi, Adaptive noise reduction algorithm for speech enhancement. Int. J. Electr. Commun. Eng. 8(6), 1014–1021 (2014). https://doi.org/10.12988/ams.2014.45365

    Article  Google Scholar 

  25. R.E. Kalman, A new approach to linear filtering and prediction problems. Am. Soc. Mech. Eng. 82(1), 35–45 (1960). https://doi.org/10.1115/1.3662552

    Article  MathSciNet  Google Scholar 

  26. N. Kalouptsidis, S. Theodoridis, Adaptive system identification and signal processing algorithms (Prentice-Hall Inc, Upper Saddle River, 1993)

    Google Scholar 

  27. G. Kim, H. Lee, J. Chung, J. Lee, A delay relaxed RLS-DCD algorithm for real-time implementation. IEEE Trans. Circuits Syst. II Express Briefs 65(1), 61–65 (2017). https://doi.org/10.1109/TCSII.2017.2706367

    Article  Google Scholar 

  28. R. Kono, M. Komatsu, H.Matsumoto (2022), Higher convergence adaptive equalization method with noise removal function using total least squares method. in 21st International Symposium on Communications and Information Technologies (ISCIT) IEEE, (2022), p. 307–311. https://doi.org/10.1109/ISCIT55906.2022.9931266

  29. J. Krolik, M. Joy, S. Pasupathy, M. Eizenman, A comparative study of the LMS adaptive filter versus generalized correlation method for time delay estimation. IEEE Int Conf Acoust, Speech, Signal Process. 9, 652–655 (1984). https://doi.org/10.1109/ICASSP.1984.1172302

    Article  Google Scholar 

  30. W.C. Lee, C.C Jay Kuo, Musical onset detection based on adaptive linear prediction, in IEEE International Conference on Multimedia and Expo. IEEE, (2006), p. 957–960. https://doi.org/10.1109/ICME.2006.262679

  31. S.H. Leung, C.F. So, Gradient-based variable forgetting factor RLS algorithm in time-varying environments. IEEE Trans. Signal Process. 53(8), 3141–3150 (2005). https://doi.org/10.1109/TSP.2005.851110

    Article  MathSciNet  Google Scholar 

  32. A.C. Mugdha, F.S. Rawnaque, M.U. Ahmed, A study of recursive least squares (RLS) adaptive filter algorithm in noise removal from ECG signals, in International Conference on Informatics, Electronics & Vision (ICIEV) IEEE, (2015), p. 1–6. https://doi.org/10.1109/ICIEV.2015.7333998

  33. V.H. Nascimento, Y.V. Zakharov, RLS adaptive filter with inequality constraints. IEEE Signal Process. Lett. 23(5), 752–756 (2016). https://doi.org/10.1109/LSP.2016.2551468

    Article  Google Scholar 

  34. C. Paleologu, J. Benesty, S. Ciochină, A practical variable forgetting factor recursive least-squares algorithm, in 11th International symposium on electronics and telecommunications (ISETC). IEEE, (2014), p. 1–4. https://doi.org/10.1109/ISETC.2014.7010812

  35. R. Pogula, T.K. Kumar, A novel RLS based adaptive filtering method for speech enhancement. World Acad. Sci., Eng.Technol., Int. J. Electr., Comput., Electron. Commun. Eng. 9(2), 153–158 (2015). https://doi.org/10.5281/zenodo.1099384

    Article  Google Scholar 

  36. P. Prandoni, V. Martin, An FIR cascade structure for adaptive linear prediction. IEEE Trans. Signal Process. 46(9), 2566–2571 (1998). https://doi.org/10.1109/78.709548

    Article  Google Scholar 

  37. N.G. Prelcic, P.G. Fernando, M. Elena Domı́nguez Jiménez, Wavelet packet-based subband adaptive equalization. Signal Process. 81(8), 1641–1662 (2001). https://doi.org/10.1016/S0165-1684(01)00077-9

    Article  Google Scholar 

  38. L. Rugini, L. Geert, Basis expansion adaptive filters for time-varying system identification, in 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing. IEEE, (2007), p. 153–156. https://doi.org/10.1109/CAMSAP.2007.4497988

  39. A.G. Rusu, S. Ciochina, C. Paleologu, J. Benesty, Cascaded RLS adaptive filters based on a Kronecker product decomposition. Electronics 11(3), 409 (2022). https://doi.org/10.3390/electronics11030409

    Article  Google Scholar 

  40. S. Song, J.S. Lim, S.J. Baek, K.M. Sung, Gauss Newton variable forgetting factor recursive least squares for time varying parameter tracking. Electron. Lett. 36(11), 988–990 (2000). https://doi.org/10.1049/el:20000727

    Article  Google Scholar 

  41. K.L. Sudha, Performance analysis of new time varying LMS (NTVLMS) adaptive filtering algorithm in noise cancellation system, in International Conference on Communication, Information & Computing Technology (ICCICT) IEEE, (2015), p. 1–6. https://doi.org/10.1109/ICCICT.2015.7045710

  42. R.K. Thenua, S.K. Agarwal, Simulation and performance analysis of adaptive filter in noise cancellation. Int. J. Eng. Sci. Technol. 2(9), 4373–4378 (2010)

    Google Scholar 

  43. H.X. Wen, S.Q. Yang, Y.Q. Hong, H. Luo, A partial update adaptive algorithm for sparse system identification. IEEE/ACM Trans. Audio, Speech, Lang. Process. 28, 240–255 (2019). https://doi.org/10.1109/TASLP.2019.2949928

    Article  Google Scholar 

  44. B. Widrow, R.E. Kalman, N. DeClaris, Adaptive Filters-Aspects of Network and System Theory (Holt Rinehart and Winston, New York, 1971), pp.563–586

    Google Scholar 

  45. B. Widrow, W. Eugene, Adaptive signal processing for adaptive control. IEEE Int Conf. Acoust., Speech, Signal Process., 9, 191–194 (1984). https://doi.org/10.1109/ICASSP.1984

    Article  Google Scholar 

  46. B. Widrow, J.R. Glover, J.M. McCool, J. Kaunitz, C.S. Williams, R.H. Hearn, J.R. Zeidler, J.E. Dong, R.C. Goodlin, Adaptive noise cancelling: principles and applications. Proc. IEEE 63(12), 1692–1716 (1975). https://doi.org/10.1109/PROC.1975.10036

    Article  Google Scholar 

  47. N.R. Yousef, H.S. Ali, Fixed-point steady-state analysis of adaptive filters. Int. J. Adapt. Control Signal Process. 17(3), 237–258 (2003). https://doi.org/10.1002/acs.738

    Article  Google Scholar 

  48. Z. Zalevsky, M. David, Fractional wiener filter. Appl. Opt. 35(20), 3930–3936 (1996). https://doi.org/10.1364/AO.35.003930

    Article  Google Scholar 

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  1. Department of Electronics and Communication Engineering, Motilal Nehru National Institute of Technology, Allahabad, Prayagraj, 211004, India

    Nilesh Kumar Yadav, Amit Dhawan, Manish Tiwari & Sumit Kumar Jha

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Yadav, N.K., Dhawan, A., Tiwari, M. et al. Modified Model of RLS Adaptive Filter for Noise Cancellation. Circuits Syst Signal Process 43, 3238–3260 (2024). https://doi.org/10.1007/s00034-024-02605-5

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